A contour of the magnetic potential U U\,U in a specialized laboratory setup is modeled by the curve with equation
x5y+4xy5=130 x^5 y + 4x y^5 = 130 x5y+4xy5=130Prove that the curve does not intersect the coordinate axes.
Show that
dydx=−5x4y+4y5x5+20xy4 \frac{dy}{dx} = -\frac{5x^4 y + 4y^5}{x^5 + 20xy^4} dxdy=−x5+20xy45x4y+4y5Prove that the curve has no stationary points.
In the case when x>0x > 0x>0, find the equation of the tangent line to the curve at the point where y=2y = 2y=2. Give your answer in the form ay+bx=cay + bx = cay+bx=c, where a,b,c a, b, c\,a,b,c are integers.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
